SIGHTED TFC LOST IN ATA. NMAC.

Narrative

ON DEP FROM ZZZ ARPT AT APPROX XY10; I HAD A NEAR NMAC WHILE FLYING. WE HAD A PATIENT ON BOARD ('LIFEGUARD' STATUS) AND THE WX WAS VFR (CLR; VISIBILITY GREATER THAN 10 MI). AFTER TAKING OFF STRAIGHT OUT RWY 31; I REMEMBER HEARING TWR GIVE ANOTHER ACFT (WHO'D APPARENTLY TAKEN OFF RWY 26) MY POS; AND HE REPLIED THAT HE HAD ME IN SIGHT. I CAN'T REMEMBER IF TWR ADVISED ME OF HIS POS -- I DON'T THINK SO. ABOUT 2 MIN LATER MY FLT NURSE (IN THE BACK) CALLED TFC AT OUR 8 OR 9 O'CLOCK POS. I SAW A TWIN ABOUT 1/4 MI AWAY CLBING AND TURNING (GRADUALLY) INTO ME FROM MY L. EXPECTING THAT THIS WAS THE GUY WHO 'HAD ME IN SIGHT' I HELD COURSE IN A SLIGHT CLB AT ROUGHLY 2000 FT) AND QUESTIONED TWR ABOUT HIM. THEY ADVISED ME HE'D SWITCHED TO DEP. SO I STARTED A DSCNT BEFORE HE CROSSED RIGHT OVER ME APPROX 200-300 FT ABOVE US. THE TIME FROM WHEN I FIRST SPOTTED HIM UNTIL HE PASSED OVERHEAD WAS APPROX 20 SECONDS. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR STATES PATIENT WAS ON BOARD FOR AN INTERFACILITY TRANSFER BUT DID NOT INFLUENCE PLT'S DECISION PROCESSES OR CONTRIBUTE TO INCIDENT.